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Chinese Remainder Approximation Theorem
[article]

2016
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arXiv
*
pre-print

We study a topological generalization of ideal co-maximality in topological rings and present some of its properties, including a generalization of the

arXiv:1509.02188v3
fatcat:bns4gbc35rayfas3gue47s6v2q
*Chinese**remainder**theorem*. ... Using the hyperspace uniformity, we prove a stronger version of this*theorem*concerning infinitely many ideals in supercomplete, pseudo-valuated rings. Finally we prove two interpolation*theorems*. ... Introduction This paper studies topological versions of the*Chinese**remainder**theorem*-CRT using two main concepts: topological co-maximality and the hyperspace uniformity. ...##
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Around the Chinese Remainder Theorem
[article]

2008
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arXiv
*
pre-print

We prove an explicit

arXiv:math/0412133v8
fatcat:n64ll73e3jbjjjmuwxenpbwmom
*Chinese**Remainder**Theorem*for one variable polynomials with complex coefficients, and derive some consequences. ...*Chinese**Remainder**Theorem*3. f = D q + R. ... The polynomial R(X) in the*Chinese**Remainder**Theorem*(*Theorem*8 page 6) is R(X) = D(a)=0 k+n<µa c a,k f (n) (a) n! (X − a) k+n , where c a,k is given by (4). Corollary 13. ...##
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Robustness in Chinese Remainder Theorem
[article]

2017
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arXiv
*
pre-print

*Chinese*

*Remainder*

*Theorem*(CRT) has been widely studied with its applications in frequency estimation, phase unwrapping, coding theory and distributed data storage. ... INTRODUCTION Conventional

*Chinese*

*Remainder*

*Theorem*(CRT) is to reconstruct a single integer by its residues modulo several moduli. ...

*Theorem*5. ...

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The General Chinese Remainder Theorem

1952
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The American mathematical monthly
*

THE GENERAL

doi:10.1080/00029890.1952.11988142
fatcat:5hjmvvkaoreu5d22fjsz74s66y
*CHINESE**REMAINDER**THEOREM*OYSTEIN ORE, Yale University 1. Introduction. The*Chinese**remainder**theorem*, as one knows, is one of the most useful tools of elementary number theory. ... These products are evidently the symmetric functions Mi, M2, +++ so that we can state: sere sete wea a VW 1952] THE GENERAL*CHINESE**REMAINDER**THEOREM*369*THEOREM*2. ...##
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A density Chinese Remainder Theorem
[article]

2013
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arXiv
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pre-print

*Theorem*1.1 (

*Chinese*

*Remainder*

*Theorem*). Let m 1 , . . . , m k be k positive integers, and let a 1 , . . . , a k be any k integers. ...

*Remainder*

*Theorems*. ...

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A Multivariable Chinese Remainder Theorem
[article]

2012
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arXiv
*
pre-print

The

arXiv:1206.5114v1
fatcat:ubrhu7egx5g3jh3d3hqwpo72m4
*Chinese**remainder**theorem*is the special case, where A has only one column. ... Historical background The*Chinese**remainder**theorem*(CRT) is one of the oldest*theorems*in mathematics. It has been used to calculate calendars as early as the first century AD [5, 22] . ... The original paper of January 27, 2005 (google "multivariable*chinese**remainder*") had been written in the context of multidimensional Diophantine approximation and was part of a talk on April 11, 2005 ...##
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The General Chinese Remainder Theorem

1952
*
The American mathematical monthly
*

THE GENERAL

doi:10.2307/2306804
fatcat:qlrc54qbznc7hggkfzvgrly2ha
*CHINESE**REMAINDER**THEOREM*OYSTEIN ORE, Yale University 1. Introduction. The*Chinese**remainder**theorem*, as one knows, is one of the most useful tools of elementary number theory. ... The*remainder**theorem*. Let the system of congruences (1) be given where it is not assumed that the moduls are necessarily relatively prime. ...##
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On Solving a Generalized Chinese Remainder Theorem in the Presence of Remainder Errors
[article]

2017
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arXiv
*
pre-print

In estimating frequencies given that the signal waveforms are undersampled multiple times, Xia et. al. proposed to use a generalized version of

arXiv:1409.0121v4
fatcat:rjvrhdxhjbderlyju6zt5527cm
*Chinese**remainder**Theorem*(CRT), where the moduli are $M_ ... This approach also reveals some useful information about the*remainders*by inspecting extreme values of the erroneous*remainders*modulo $4\tau$. ... Introduction The usual*Chinese**Remainder**Theorem*(CRT) concerns reconstructing an integer given its*remainders*with respect to a set of coprime moduli. ...##
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Multi-Stage Robust Chinese Remainder Theorem

2014
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IEEE Transactions on Signal Processing
*

It is well-known that the traditional

doi:10.1109/tsp.2014.2339798
fatcat:jkslbxydvndtlhvwbnhkxjk66a
*Chinese**remainder**theorem*(CRT) is not robust in the sense that a small error in a*remainder*may cause a large error in the reconstruction solution. ... In this special case, a closed-form reconstruction from erroneous*remainders*was proposed and a necessary and sufficient condition on the*remainder*errors was obtained. ... Multi-Stage Robust*Chinese**Remainder**Theorem*Li Xiao, Xiang-Gen Xia, Fellow, IEEE, and Wenjie Wang, Member, IEEE Abstract-It is well-known that the traditional*Chinese**remainder**theorem*(CRT) is not robust ...##
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A Chinese Remainder Theorem for Partitions
[article]

2022
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arXiv
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pre-print

We present an analogue of the

arXiv:2105.07611v2
fatcat:kcdkntvdufhudlbcmkkdsdvrzy
*Chinese**Remainder**Theorem*in this paper. Write C t for the set of t-cores. ... By the usual*Chinese**Remainder**Theorem*, we may view Z/mZ as the fibre product of Z/sZ and Z/tZ over Z/dZ. So we then investigate the effect of the functor S S k on a fibre product. ... We recall*Theorem*3 from the Introduction.*Theorem*3. If core d (σ) = core d (τ ), then there is a quasipolynomial Proof. Let i ≥ ℓ 0 . ...##
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Equidistribution from the Chinese Remainder Theorem
[article]

2020
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arXiv
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pre-print

We prove the equidistribution of subsets of (/)^n defined by fractional parts of subsets of (/q)^n that are constructed using the

arXiv:2003.12965v2
fatcat:yjtwlkfvsfbevkxywto4hzjbui
*Chinese**Remainder**Theorem*. ... These sets A q are built out of the sets A p v for prime powers p v using the*Chinese**Remainder**Theorem*. ... In this paper we show that Hooley's result may be recast as a general fact concerning the equidistribution of sets arising from the*Chinese**Remainder**Theorem*. ...##
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Equidistribution from the Chinese Remainder Theorem

2021
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Advances in Mathematics
*

These sets A q are built out of the sets A p v for prime powers p v using the

doi:10.1016/j.aim.2021.107776
fatcat:dowri2q7oja6vbqpm7cdgetr54
*Chinese**Remainder**Theorem*. ... In this paper we show that Hooley's result may be recast as a general fact concerning the equidistribution of sets arising from the*Chinese**Remainder**Theorem*. ... By the*Chinese**Remainder**Theorem*α(x) is bounded by the product over p v q of the number of solutions to h · x = h · y (mod p v ), and this may be bounded by (p v ) if h ≡ 0 (mod p v ) and the resulting ...##
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Chinese remainder theorems and Galois modules

1986
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Journal of the Australian Mathematical Society
*

In particular, the paper seeks to establish a relationship between Galois submodules of L and certain types of

doi:10.1017/s1446788700027257
fatcat:6dgpedrhofgpdii64d62qsa4b4
*Chinese**Remainder**Theorems*. 1980 Mathematics subject classification (Amer. Math. ... By the*Chinese**Remainder**Theorem*for L we have K V ® K L= 0 L w (cf. [2, pages 54 ff]). ... I 2 1*Chinese**Remainder**Theorems*and Galois Modules 277*THEOREM*Let L be a finite normal extension of K, with K a finite algebraic extension of Q, and let G = G(L/K). ...##
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Poisson statistics via the Chinese remainder theorem
[article]

2005
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arXiv
*
pre-print

We consider the distribution of spacings between consecutive elements in subsets of Z/qZ where q is highly composite and the subsets are defined via the

arXiv:math/0412135v2
fatcat:yxwixjmksvb4neou55k2lec5ni
*Chinese**remainder**theorem*. ... We also study the spacings of subsets of Z/q_1q_2Z that are created via the*Chinese**remainder**theorem*from subsets of Z/q_1Z and Z/q_2Z (for q_1,q_2 coprime), and give criteria for when the spacings modulo ... Here we give several examples to indicate when we cannot expect some kind of "Central limit*theorem*" for the*Chinese**remainder**theorem*! 6.1. Counterexample 1. ...##
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Computing Hilbert class polynomials with the Chinese remainder theorem

2010
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Mathematics of Computation
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We present a space-efficient algorithm to compute the Hilbert class polynomial H_D(X) modulo a positive integer P, based on an explicit form of the

doi:10.1090/s0025-5718-2010-02373-7
fatcat:bthdblwvvzgofhyrigrz46oowm
*Chinese**Remainder**Theorem*. ... Our algorithm is based on the CRT approach [1, 5, 17] , which computes the coefficients of H D modulo many "small" primes p and then applies the*Chinese**Remainder**Theorem*(CRT). ... We now suppose we have computed H D modulo primes p 1 , . . . , p n and consider how to compute H D mod P for an arbitrary positive integer P , using the*Chinese**Remainder**Theorem*. ...
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